On the odd-even property of functions for boundary currents over kz in a spectrum of two-dimensional solutions

When a spectrum of two-dimensional (2-D) solutions (S2DS) is applied to calculate the far-field functions or impedances of three-dimensional (3-D) elements in the vicinity of two-dimensional (2-D) structures, in general, the calculations have to be performed for both positive and negative values of k_z. This letter analyzes the odd-even property of functions for boundary currents over k_z. Therefore, by using this odd-even property, the calculations of the far-field functions and impedances are only needed to be performed for positive values of k_z, which reduces the computation cost by a factor of 2. A verification case is also presented.